energy harvesting from ambient vibrationsenergy harvesting from ambient vibrations fr´ed´eric...

IntroductionModelling of a piezoelectric energy harvester

An Example of inverter

Energy Harvesting from Ambient Vibrations

Frederic Giraud

L2EP – University Lille1

November 27, 2012

Frederic Giraud Master E2D2 University Lille1 - L2EP



Table of contents

1 IntroductionWhat is Energy Harvesting ?Generator TechnologiesSummary

2 Modelling of a piezoelectric energy harvesterPresentation of the systemEMR of the systemPower Extraction on a load resistor RL from harmonic oscillation

3 An Example of inverterIntroductionSSHI: Synchronized Switch Harvesting on Inductor

Frederic Giraud Master E2D2 November 27, 2012 2 / 40



What is Energy Harvesting ?Generator TechnologiesSummary

What is Energy Harvesting ?

We extract energy from an ambient and free source:







−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE







−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion







−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

LOAD







−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

LOAD

P1 P2







−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

LOAD

P1 P2

We talk about Energy Harvesting or also energy scavenging

when the converted power is small, typically less than 1W.







−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

LOAD

P1 P2

We talk about Energy Harvesting or also energy scavenging

when the converted power is small, typically less than 1W.

η = P2P1

= 1− P1−P2P1

−→ Losses in the energy converter should be

as small as possible.





Objectives: Sensors Network

www.perpetuum.com






www.perpetuum.com

Gutierriez,A Heterogeneous Wireless IdentificationNetwork for the Localization of Animals Based onStochastic Movements






www.perpetuum.com

Gutierriez,A Heterogeneous Wireless IdentificationNetwork for the Localization of Animals Based onStochastic Movements

http://www.rfwirelesssensors.com, 2012

Roundy et Al.:A study of low level vibrations as a powersource for wireless sensor nodes.





Objectives: Power, just where you need it

http://enocean.com

Wireless

Reduce Cost, and isreconfigurable

Better Waste Cycle(Information fromEnocean)






http://enocean.com

Wireless



Innowattech’s systems produces power with vehicles

http://www.innowattech.com






http://enocean.com

Wireless



Innowattech’s systems produces power with vehicles

http://www.innowattech.com

The economist – April 28th 2007





Objectives: Marketing Purpose

Experience: Same Remotecontroller energized by humanpower, but with different packaging.

”No need for Batteries”

”Green” ”Fun”









54% of people Will choose the firstone because it is eco-friendly.(Jansen, Human power empirically explored)









54% of people Will choose the firstone because it is eco-friendly.(Jansen, Human power empirically explored)

Several projects are born fromthis fact: Metis Produces energyfrom dancers’ movements.

In Toulouse, the system VIHA

proposes Smart Tiles to energiesstreet lights.





The energy converter

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD






−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

︷︸︸︷

EnergyConversion

ElectricityElec.






−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

︷︸︸︷

EnergyConversion

ElectricityElec.

Generator






−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

︷︸︸︷

EnergyConversion

ElectricityElec.

Generator Inverter





Solar Harvesters:





Solar Harvesters:

This sensor measures IntraOccular Pres-sure http://cymbet.com

Handbag to recharge electronicdevices http://www.neubers.de





Solar Harvesters:



Solar Energy Harvester Evaluation Kit http://ti.com

Power and current asa function of voltage:

I,P

V





Solar Harvesters:



Solar Energy Harvester Evaluation Kit http://ti.com

Power and current asa function of voltage:

I,P

VMPPT strategies,require Energymanagement of thesystem





Thermoelectric

A Peltier module from http://www.tellurex.com

VDC

RDC IDC





Thermoelectric


VDC

RDC IDC

IDC

VDC

IDC

P

T1





Thermoelectric


VDC

RDC IDC

IDC

VDC

IDC

P

T1 T2





Thermoelectric


VDC

RDC IDC

IDC

VDC

IDC

P

T1 T2

=

=





Thermoelectric


VDC

RDC IDC

IDC

VDC

IDC

P

T1 T2

=

=

Temperature Gradient (residential). Lindsay Miller,http://uc-ciee.org

plumbing application from http://www.nextreme.com





Magnetic

stoppercoilstopper

φx





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vB





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vB=

∼





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vB





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i

1

1) Diode turns ON





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i

1 2

1) Diode turns ON2) di

dt= 0 because e − vB = 0





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i

1 2

3



3) i = 0, diode turns OFF





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i

1 2

3〈i〉



3) i = 0, diode turns OFF





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i

1 2

3〈i〉



3) i = 0, diode turns OFF vB

〈i〉, P





Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vBt

e,vB, i

1 2

3〈i〉




〈i〉, P

P = 〈vB i〉 = vB〈i〉Frederic Giraud Master E2D2 November 27, 2012 10 / 40




Magnetic

stoppercoilstopper

φx

e = −N dφdt

= N dφdx

dxdt

v

e(t)

L i

vB=

∼t

e,vB, i

1 2

3〈i〉




〈i〉, P

P = 〈vB i〉 = vB〈i〉Frederic Giraud Master E2D2 November 27, 2012 10 / 40




Piezoelectric

An electronic lighter,http://freepatentsonline.com

Piezoelectric crystals





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

vim

im is a current proportionalto the deformation speed





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)


vim

im is a current proportionalto the deformation speedComparison Magn. Piezo

Magnetic Piezo.Voltage source Current

sourceInductive capacitiveLarge Stroke Small

StrokeRemote action





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)


vim




StrokeRemote action

Roundy, A piezoelectric vibrationbased generator for wireless

electronics (2004)





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)


vim RL




StrokeRemote action


electronics (2004)





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)


vim RL




StrokeRemote action


electronics (2004)

ω

P

ω0





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)


vim RL




StrokeRemote action


electronics (2004)

ω

P

ω0

RLopt

PMax

RL

P





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)

Energy ManagementEquivalent electrical circuit

vim RL




StrokeRemote action


electronics (2004)

ω

P

ω0

RLopt

PMax

RL

P





Piezoelectric



Cantilever beam

w(t) = Wsin(ωt)

Energy ManagementEquivalent electrical circuit

vim RL

=

∼




StrokeRemote action


electronics (2004)

ω

P

ω0

RLopt

PMax

RL

P





There is no ”one fit all” solution

Each solution may be efficient in a certain range of Power.Meanwhile, shrinking Chips consumption come at a time when energy harvesting becomes efficient and practical

(source: IDtechex.com)





Table of contents







Presentation of the systemEMR of the systemPower Extraction on a load resistor RL from harmonic oscillation

Coordinates and assumptions

moving Case

Bender






moving Case

Bender

The bender is attached to a vibrating andrigid case,






moving Case

BenderM


A mass M is attached to increase powerharvesting,






moving Case

BenderM

w(t)



w(t) is the deflection of the beam,






moving Case

BenderM

w(t)

ℜ




We define ℜ a fixed reference frame,






moving Case

BenderM

w(t)

ℜℜ′





And ℜ′ a reference frame affixed to thevibrating case.






moving Case

Bender

−→F p→M

Mw(t)

ℜℜ′






−→F p→m is the force of the Bender onto themass M.






moving Case

Bender

−→F p→M

Mw(t)

ℜℜ′







The case is supposed to be controlled inposition, and we have yc = Asin(ωt) theamplitude of the case’s vibration.






moving Case

Bender

−→F p→M

Mw(t)

ℜℜ′








Gravity is neglected, as well as Inertiamomentum of the bender,






moving Case

Bender

−→F p→M

Mw(t)

ℜℜ′

vim

i








Gravity is neglected, as well as Inertiamomentum of the bender,

Actuator electrical convention.





Equations

Dynamic of the mass M: Glossary

M the mass

f , the force onto M

A, vibration’s amplitude

ω, vibration’s pulsation

facc is the inertial force

i current of the device(actuator convention)

im motional current

fp inside piezo force

N Piezoelectric forcefactor (depends ongeometry)

fp Piezo internal force

fs Material internal elasticforce

Ks equivalent stiffness(depends on geometry)

Ds Viscous coefficient





Equations

Dynamic of the mass M:

M d2

dt2(w(t) + Asin(ωt)) = Fp→M = f

Glossary

M the mass






im motional current











Equations


M d2


Mw(t) = f +MAω2sin(ωt) = f + facc

Glossary

M the mass






im motional current











Equations


M d2



Electrical Behaviour: Capacitive

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt

Piezoelectric effect

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt


im derives from deflection: im = Nw

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt



while v produces an internal forcefp = Nv

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt




Material’s behaviour

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt





The material is elastic: fs = Ks

∫wdt

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt






∫wdt

With some friction inside:fs = Ks

∫wdt + Ds w

Glossary

M the mass






im motional current











Equations


M d2




v = 1Cb

∫(i − im)dt






∫wdt

With some friction inside:fs = Ks

∫wdt + Ds w

These actions are opposite to the PEeffect: f = fp − fs

Glossary

M the mass






im motional current











EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

vSE





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw

w

fp

w

f

w =1

M

∫

(f − facc )dt

︸︷︷︸





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw

w

fp

w

f

w =1

M

∫

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

∫

wdt + Ds w

w

fs





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw

w

fp

w

f

w =1

M

∫

(f − facc )dt

︸︷︷︸

facc

w

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

∫

wdt + Ds w

w

fs

SM





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw

w

fp

w

f

w =1

M

∫

(f − facc )dt

︸︷︷︸

facc

w

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

∫

wdt + Ds w

w

fs

SM

pe = v .i is the output power,





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw

w

fp

w

f

w =1

M

∫

(f − facc )dt

︸︷︷︸

facc

w

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

∫

wdt + Ds w

w

fs

SM

pe = v .i is the output power, pm = facc w is the mechanical input power

and both should be < 0





EMR of the system

v =1

Cb

∫

(i − im)dt

︸︷︷︸

i

v im

v

SE

︷︸︸︷

fp = Nv, im = Nw

w

fp

w

f

w =1

M

∫

(f − facc )dt

︸︷︷︸

facc

w

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

∫

wdt + Ds w

w

fs

SM

pe = v .i is the output power, pm = facc w is the mechanical input power

and both should be < 0

v

i e

i

SE Ω

T

Tr

Ω

SM Comparison with a DC motor

Things are not so differerent.





Asumption

facc = MAω2sin(ωt) for harmonic oscillations





Asumption


complex notation: x is the complex phasor of x(t), meansx(t) = ℑ(x)





Asumption


complex notation: x is the complex phasor of x(t), meansx(t) = ℑ(x)since oscillations are harmonic, we will write:x = Xe jωt





Asumption



for steady state operation, X is constant, leading todxdt

= jωXe jωt





Asumption




= jωXe jωt

|x | = |X | = X





Asumption




= jωXe jωt

|x | = |X | = X

for example, f acc = MAω2e jωt and |f acc | = MAω2.





Asumption




= jωXe jωt

|x | = |X | = X


v = −RLi





Asumption




= jωXe jωt

|x | = |X | = X


v = −RLi

v RLim

i





Asumption




= jωXe jωt

|x | = |X | = X


v = −RLi

v RLim

i And RL ≪ 1Cbω

, yieldsv ≃ −RLim





For an ideal generator (Ds = 0)

Mw = f + f acc






Mw = f + f acc

f = Nv − Ksw






Mw = f + f acc

f = Nv − Ksw

v = −RLim = −RLNw






Mw = f + f acc

f = Nv − Ksw


Mw + N2RLw + Ksw = f acc






Mw = f + f acc

f = Nv − Ksw


Mw + N2RLw + Ksw = f acc−→ RL acts as a damping

P2 = − 12RL|im|2






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2

|im| = N |w | = ω.N.|facc|√(Ks−Mω

2)2+(N2RLω)2






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2

(Ks−Mω2)2+(N2RLω)2






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


ω

P2






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


ω

P2

ω0

P2max






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


ω

P2

ω0

P2max

The vibrations should occur atgenerator’s resonance frequency

ω0 =√

KsM






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


ω

P2

ω0

P2max RL ց


ω0 =√

KsM






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL

P2max






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL

P2max

We can harvest as muchpower as we want






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL

P2max







Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL

P2max ,Wmax







Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL

P2max ,Wmax

We can harvest as muchpower as we want, at theexpense of largedisplacement of thebender’s tip






Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL

P2max ,WmaxTechnological limit for Wmax







Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL,

vmax = MAω2

N

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL








Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL,

vmax = MAω2

N

P1Max = 12 faccωWMax = (MAω2)2

N2RL= P2Max

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL








Mw = f + f acc

f = Nv − Ksw



P2 = − 12RL|im|2


2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

2


P2Max = (MAω2)2

2N2RL, Wmax = MAω

N2RL,

vmax = MAω2

N

P1Max = 12 faccωWMax = (MAω2)2

N2RL= P2Max

ω

P2

ω0

P2max RL ց


ω0 =√

KsM

RL


Assumtionnot valid






For a real generator (Ds 6= 0)

f = Nv − Ksw − Dsw







w =f acc

(Ks−Mω2)+jω(Ds+N2RL)







w =f acc


P2 = − 12RL|im|2







w =f acc


P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2







w =f acc


P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

∗)







w =f acc


P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

∗)

P1 = − 12


2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

ω

|w |

ω

P2, P1







, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2





Example

Device’s properties

N = 0.012N/V , Ks = 6300N/m, Cb = 300nF , Ds = 0.17Ns/m,M = 1g

Calculate for A = 0.1mm

the best working frequency,

the harvested P2 power in the bestcase,

the power of the source P1 in suchbest case,

the optimal resistor RL,

the deflection amplitude of the bender,

the voltage for this working point.

Validation

Is v = −RLim a validassumption?





Answers

The best working frequency is given by

f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz





Answers


f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz

For the best case, P2 is given by

P2 =|f acc |

2

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW





Answers


f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz


P2 =|f acc |

2

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

For the best case P1 = 2.P2 = 928mW





Answers


f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz


P2 =|f acc |

2

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW


The optimal resistor RLopt is given byRLopt =

Ds

N2 = 0,170,0122

= 1180Ω





Answers


f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz


P2 =|f acc |

2

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW



Ds

N2 = 0,170,0122

= 1180Ω

The deflection Wmax is given by


= (1.10−3.1.10−4.(2π.400)2)2.0,17.2π.400 = 738µm!





Answers


f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz


P2 =|f acc |

2

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW



Ds

N2 = 0,170,0122

= 1180Ω



= (1.10−3.1.10−4.(2π.400)2)2.0,17.2π.400 = 738µm!

The voltage is then given byvmax = NRLω0|w | = 0, 012.1180.2π.400.738.10−6 = 26V





Answers


f0 =12π

√Ks

M= 1

2π

√63001.10−3 = 400Hz


P2 =|f acc |

2

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW



Ds

N2 = 0,170,0122

= 1180Ω



= (1.10−3.1.10−4.(2π.400)2)2.0,17.2π.400 = 738µm!

The voltage is then given byvmax = NRLω0|w | = 0, 012.1180.2π.400.738.10−6 = 26V

ZCb = 1Cbω

= 12π.400.300.10−9 = 1990Ω ≈ RL, −→ Calculations

are NOT valid!





For a real Generator, Ds 6= 0 and v 6= −RLim

v RLim

i






v RLim

i

We can show:v = − RL

1+jωRLCbim = −jωNRL

1−jωRLCb

1+(RLCbω)2wm

and we write: v = −jωNrLeqw − Nkeqw






v RLim

i



1−jωRLCb

1+(RLCbω)2wm


2 Cases to consider, since ω should be ω0:






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb

rLeq ≃ RL and kLeq ≃ 0, no problem,just use the assumption






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb


ω0 ≫ 1RLCb






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb


ω0 ≫ 1RLCb

ω

rLeq |dB , kLeq |dB






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb


ω0 ≫ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb


ω0 ≫ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb

rLeq ≪ RL and kLeq is high, an otherstudy is needed






v RLim

i



1−jωRLCb

1+(RLCbω)2wm



ω0 ≪ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb


ω0 ≫ 1RLCb

ω

rLeq |dB , kLeq |dB

ω01

RLCb

rLeq ≪ RL and kLeq is high, an otherstudy is needed

((Ks + N2keq)−Mω2) + jω(Ds + N2rLeq)w = f accFrederic Giraud Master E2D2 November 27, 2012 23 / 40




Rule of the Thumb

Let Rb defined as RbCbω0 = 1, ω0 <1

RLCb→ RL < Rb

ω

P2/P2max

ω0

RL

P2/P2Max

RLopt





Rule of the Thumb


RLCb→ RL < Rb

ω

P2/P2max

ω0

RL

P2/P2Max

RLopt

Rb1





Rule of the Thumb


RLCb→ RL < Rb

ω

P2/P2max

ω0

RL

P2/P2Max

RLopt

Rb1

rL ≃ RL ; keq ≃ 0 rL < RL ; keq ր





Rule of the Thumb


RLCb→ RL < Rb

ω

P2/P2max

ω0

RL

P2/P2Max

RLopt

Rb1Rb2






Rule of the Thumb


RLCb→ RL < Rb

ω

P2/P2max

ω0

RL

P2/P2Max

RLopt

Rb1Rb2Rb3






Rule of the Thumb


RLCb→ RL < Rb

ω

P2/P2max

ω0

RL

P2/P2Max

RLopt

Rb1Rb2Rb3Rb4






Partial Conclusion

If Ropt < Rb

A resistor can recover the power optimally. But the study was notvalid for high RL. What happens for RL ≫ Rb?





Partial Conclusion

If Ropt < Rb

A resistor can recover the power optimally. But the study was notvalid for high RL. What happens for RL ≫ Rb?

If Ropt > Rb

The power is not well extracted because P2 < P2max . Thishappens for high damped mechanisms.A simple resistor cannot recover the power optimally (and this isdue to Cb).





What happens if Ropt < Rb and RL ≫ Rb?

resonance is shifted

rLeq = RL

1+(RLCbω)2≃ RL

(RLCbω)2

keq = RLω2RLCb

1+(RLCbω)2≃ 1

Cb

((Ks + N2keq)−Mω2) + jω(Ds + N2rLeq)w = f acc leads to:

ω′0 =

√Ks+N2keq

M=

√

Ks+N2

Cb

M






resonance is shifted

rLeq = RL

1+(RLCbω)2≃ RL

(RLCbω)2

keq = RLω2RLCb

1+(RLCbω)2≃ 1

Cb

((Ks + N2keq)−Mω2) + jω(Ds + N2rLeq)w = f acc leads to:

ω′0 =

√Ks+N2keq

M=

√

Ks+N2

Cb

M

Another optimal resistor

The optimal power is harvested is N2rLeq = Ds , leading to:N2RL

(RLCbω′0)

2 = N2

RLC2b

Ks+N2Cb

M

= Ds

RLopt2 = N2

Ds

1

C2bKsM

(1+ N2

KsCb)=

R2b

RLopt

1

1+ N2

KsCb






RLopt

RL(log)

P2/P2Max






RLopt

RL(log)

P2/P2Max

RLopt2





Conclusion

For the realistic case, there is one or two resistive loads whichallow to extract the maximum of power,

RLopt

RL(log)

P2/P2Max

RLopt2





Conclusion


There exist an optimal frequency which may vary if RL is veryhigh,

RLopt

RL(log)

P2/P2Max

RLopt2

ω

P2/P2max

ω0





Conclusion



For highly damped structure, a simple resistor is not optimal.

RLopt

RL(log)

P2/P2Max

RLopt2

ω

P2/P2max

ω0 ≃ N2

Cbω0

Ds

P2/P2Max





Conclusion



For highly damped structure, a simple resistor is not optimal.

→ we always want to harvest the maximum of power!

RLopt

RL(log)

P2/P2Max

RLopt2

ω

P2/P2max

ω0 ≃ N2

Cbω0

Ds

P2/P2Max





Table of contents







IntroductionSSHI: Synchronized Switch Harvesting on InductorConclusion

Introduction

v

imRL=

∼





Introduction

v

imRL





Introduction

v

imRL

im > 0





Introduction

v

imRL

im > 0v

imRL

vL





Introduction

v

imRL

im > 0v

imRL

vL

vL = RLim which is > 0and v = −vL = −RLim





Introduction

v

imRL

im > 0v

imRL

vL


im < 0





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL

vL = −RLim which is > 0again, and

v = vL = −RLim





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM

The current is rectified, but we still havev = −RLim: Power harvesting depends on RL





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM


Moreover, it is still not optimal if Ropt > Rb.





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM


Moreover, it is still not optimal if Ropt > Rb.This is why, some want to compensate for Cb:





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM



v

imRL

vL





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM



v

imRL

vL

This is a bad solution because it works only forω0 (what if the frequency shifts?), and theInductor is large (because ω0 usually is small)





Introduction

v

imRL

im > 0v

imRL

vL


im < 0v

imRL

vL


v = vL = −RLim

time

T0 = 1

2π

√

KsM



v

imRL

vL

This is a bad solution because it works only forω0 (what if the frequency shifts?), and theInductor is large (because ω0 usually is small)−→Non linear Techniques





Why Synchronized





Why Synchronized

SE v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM





Why Synchronized

SE

H bridge

v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM





Why Synchronized

SE v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM

Strategy: v = −Ropt im leads tofpN= −Ds

N2Nw or, fp = −Dsw .





Why Synchronized

SE v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM

fpref







Why Synchronized

SE v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM

fpref

vref







Why Synchronized

SE v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM

fpref

vrefiref


N2Nw or, fp = −Dsw .This shows that v should be controlled.





Why Synchronized

SE v

i

vL

iL

α

i

v im

v

w

fp

w

f

facc

w

w

fs

SM

fpref

vrefiref


N2Nw or, fp = −Dsw .This shows that v should be controlled.SSHI does this withefficiency.





How it works

LC oscillations





How it works

LC oscillations

+v

i

t = 0





How it works

LC oscillations

+v

i

t = 0

t

v , i





How it works

LC oscillations Switched inductor

+v

i

t = 0

t

v , i





How it works


+v

i

t = 0

t

v , i+v

i





How it works


+v

i

t = 0

t

v , i+v

it

v , i





How it works


+v

i

t = 0

t

v , i+v

it

v , i

SSHI





How it works


+v

i

t = 0

t

v , i+v

it

v , i

SSHI

Piezo

v

im K

iI

RLvLCF





How it works


+v

i

t = 0

t

v , i+v

it

v , i

SSHI

Piezo

v

im K

iI

RLvLCF

t

v , iI , im, vL





How it works


+v

i

t = 0

t

v , i+v

it

v , i

SSHI

Piezo

v

im K

iI

RLvLCF

t

v , iI , im, vL

on off on off on off on off

Switching is synchronized on w , or

im = Nw .





How it works


+v

i

t = 0

t

v , i+v

it

v , i

SSHI

Piezo

v

im K

iI

RLvLCF

Operating point: calculate vL from im

1st Harmonic assumption: P = 12

V 2L

RL≃ 1

2

4VLImπ

, VL = 4πRL Im

t

v , iI , im, vL



im = Nw .





How it works


+v

i

t = 0

t

v , i+v

it

v , i

SSHI

Piezo

v

im K

iI

RLvLCF

Operating point: calculate vL from im

1st Harmonic assumption: P = 12

V 2L

RL≃ 1

2

4VLImπ

, VL = 4πRL Im

SSHI controls v and synchronises it, but doesn’t impose fp = −Ds w .

t

v , iI , im, vL



im = Nw .





Conclusion

Performances

SSHI can extract energy more efficiently than a resistor whendamping is important,

Ds

P2/P2Max

SSHI

RL





Conclusion

Performances


But Power extraction still depends on the load,

Ds

P2/P2Max

SSHI

RL





Conclusion

Performances


But Power extraction still depends on the load,

Needs to measure bender’s deflection w(t).

Ds

P2/P2Max

SSHI

RL





General conclusion

In this presentation, applications of Energy Harvesting were shown.The modelling of a piezoelectric generator has shown that thepower source needs an adaptation:

in frequency,

in load.

to maximize the harvested poer.The key energy management rules were presented through theanalysis of the EMR of the system. A typical power electroniccircuit was also presented, but the bibliography shows a lot ofexample.





References I

S Adhikari, M I Friswell, and D J Inman, Piezoelectric energy harvesting from broadband random vibrations,

Smart Materials and Structures 18 (2009), no. 11, 115005.

R. G Ballas, H. F Schlaak, and A. J Schmid, Closed form analysis of piezoelectric multilayer bending

actuators using constituent equations, The 13th International Conference on Solid-State Sensors, Actuatorsand Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS ’05, vol. 1, IEEE, June 2005,pp. 788– 791 Vol. 1.

R. Djugum, P. Trivailo, and K. Graves, A study of energy harvesting from piezoelectrics using impact forces,

The European Physical Journal Applied Physics 48 (2009), no. 1, 11101.

Daniel Guyomar, Gal Sebald, Sbastien Pruvost, Mickal Lallart, Akram Khodayari, and Claude Richard,

Energy harvesting from ambient vibrations and heat, Journal of Intelligent Material Systems and Structures20 (2009), no. 5, 609 –624.

Aman Kansal, Jason Hsu, Sadaf Zahedi, and Mani B. Srivastava, Power management in energy harvesting

sensor networks, ACM Transactions on Embedded Computing Systems 6 (2007), 32–es.

Elie Lefeuvre, Adrien Badel, Claude Richard, and Daniel Guyomar, Piezoelectric energy harvesting device

optimization by synchronous electric charge extraction, Journal of Intelligent Material Systems andStructures 16 (2005), no. 10, 865 –876.

H. Lhermet, C. Condemine, M. Plissonnier, R. Salot, P. Audebert, and M. Rosset, Efficient power

management circuit: From thermal energy harvesting to above-IC microbattery energy storage, IEEEJournal of Solid-State Circuits 43 (2008), no. 1, 246–255.





References II

G. A. Lesieutre, G. K. Ottman, and H. F. Hofmann, Damping as a result of piezoelectric energy harvesting,

Journal of Sound and Vibration 269 (2004), no. 3-5, 991–1001.

D. Niyato, E. Hossain, M. M Rashid, and V. K Bhargava, Wireless sensor networks with energy harvesting

technologies: a game-theoretic approach to optimal energy management, IEEE Wireless Communications 14(2007), no. 4, 90–96.

Shad Roundy, Paul Kenneth Wright, and Jan M. Rabaey, Energy scavenging for wireless sensor networks:

with special focus on vibrations, Springer, 2003.

G. Sebald, E. Lefeuvre, and D. Guyomar, Pyroelectric energy conversion: Optimization principles, IEEE

Transactions on Ultrasonics, Ferroelectrics and Frequency Control 55 (2008), no. 3, 538–551.

Qing-Ming Wang and L. E Cross, Constitutive equations of symmetrical triple layer piezoelectric benders,

IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 46 (1999), no. 6, 1343–1351.





End of the presentation

Questions?


energy harvesting from ambient vibrationsenergy harvesting from ambient vibrations fr´ed´eric...

Documents